1. Field of the Invention
The present invention relates to a scanning optical system capable of a two-dimensional scanning.
2. Description of the Prior Art
In FIG. 1 there is schematically shown a scanning optical system comprising a reflecting surface 1 as a deflector capable of independent rotational movement about two orthogonal axes X and Y.sub.M to achieve a two-dimensional scanning, wherein the light beam 2 deflected by said deflecting surface 1 is focused by an imaging lens 3 onto a plane 4 to be scanned. In this illustration it is assumed that the axis Y.sub.M is parallel to said deflecting surface 1 and is orthogonal to a fixed axis X which is orthogonal to the optical axis of said imaging lens 3. It is further assumed that the reflecting surface 1 is in a standard rotational position with respect to said rotational axes X and Y.sub.M when said surface 1 is perpendicular to the optical axis 5 of said imaging lens 3, and that a beam deflection in the direction of axis X' on said plane 4 caused by a rotation of said reflecting surface 1 about the axis Y.sub.M is defined as a principal deflection with a principal deflection angle W.sub.1 while a deflection in the direction of axis Y' on said plane 4 caused by a rotation of said reflecting surface 1 about the axis X is defined as an auxiliary deflection with an auxiliary deflection angle W.sub.2.
It is now assumed that the optical system shown in FIG. 1 utilizes an ordinary f.multidot.tan.theta. lens which focuses a parallel beam entering said lens with an angle .theta. to the optical axis thereof at a position distant from said optical axis by y=f.multidot.tan.theta., and that said optical system receives a light beam parallel to said axis X. Now let us consider the following scanning cases of:
(1) The principal deflection angle is maintained constant (W.sub.1c, -W.sub.1c) while the auxiliary deflection angle W.sub.2 is changed (-W.sub.2c .ltoreq.W.sub.2 .ltoreq.W.sub.2c), i.e. EQU W.sub.1 =W.sub.1c, -W.sub.2c .ltoreq.W.sub.2 .ltoreq.W.sub.2c ; (i) PA1 (2) The auxiliary deflection angle W.sub.2 is maintained constant (W.sub.2c, -W.sub.2c) while the principal deflection angle W.sub.1 is changed (-W.sub.1c .ltoreq.W.sub.1 .ltoreq.W.sub.1c), i.e. EQU W.sub.2 =W.sub.2c' -W.sub.1c .ltoreq.W.sub.1 .ltoreq.W.sub.1c ; (iii) EQU W.sub.2 =-W.sub.2c, -W.sub.1c .ltoreq.W.sub.1 .ltoreq.W.sub.1c (iv)
or EQU (ii) W.sub.1 =-W.sub.1c, -W.sub.2c .ltoreq.W.sub.2 .ltoreq.W.sub.2c ; (ii)
As shown in FIG. 2, the beam trajectories on said plane to be scanned 4 corresponding to the abovementioned conditions (i), (ii), (iii) and (iv) become spool-shaped. More specifically, though the principal scan lines (beam trajectories formed in the principal scanning) are linear, the auxiliary scan lines (beam trajectories formed in the auxiliary scanning) become curved. Also the scan lines are not equally pitched even when the auxiliary deflection angle W.sub.2 is changed linearly in time.
Now, when the optical system shown in FIG. 1 receives an incident light beam parallel to the axis Y, the beam trajectories corresponding to the above-mentioned conditions (i), (ii), (iii) and (iv) on the plane to be scanned become spool-shaped as shown in FIG. 3, in which case the auxiliary scan lines become linear while the principal scan lines become curved.
Thus, as explained in the foregoing, the shape of the principal scan lines on the plane to be scanned is inevitably different from that of the auxiliary scan lines regardless whether the incident light beam is introduced parallel to the axis X or to the axis Y of the reflecting surface 1.
In case the imaging lens is composed of spherical lenses, the effect of correction of image distortion achievable by such spherical lenses appears isotropically both in the principal and auxiliary scanning directions. It is therefore necessary to achieve an optical scanning system capable of reproducing the principal and auxiliary scan lines in the same form on the plane to be scanned.